A family of variable step-size affine projection adaptive filter algorithms using statistics of channel impulse response
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RESEARCH
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A family of variable step-size affine projection adaptive filter algorithms using statistics of channel impulse response Mohammad Shams Esfand Abadi* and Seyed Ali Asghar AbbasZadeh Arani
Abstract This paper extends the recently introduced variable step-size (VSS) approach to the family of adaptive filter algorithms. This method uses prior knowledge of the channel impulse response statistic. Accordingly, optimal stepsize vector is obtained by minimizing the mean-square deviation (MSD). The presented algorithms are the VSS affine projection algorithm (VSS-APA), the VSS selective partial update NLMS (VSS-SPU-NLMS), the VSS-SPU-APA, and the VSS selective regressor APA (VSS-SR-APA). In VSS-SPU adaptive algorithms the filter coefficients are partially updated which reduce the computational complexity. In VSS-SR-APA, the optimal selection of input regressors is performed during the adaptation. The presented algorithms have good convergence speed, low steady state mean square error (MSE), and low computational complexity features. We demonstrate the good performance of the proposed algorithms through several simulations in system identification scenario. Keywords: Adaptive filter, Normalized Least Mean Square, Affine projection, Selective partial update, Selective regressor, Variable step-size
1. Introduction Adaptive filtering has been, and still is, an area of active research that plays an active role in an ever increasing number of applications, such as noise cancellation, channel estimation, channel equalization and acoustic echo cancellation [1,2]. The least mean squares (LMS) and its normalized version (NLMS) are the workhorses of adaptive filtering. In the presence of colored input signals, the LMS and NLMS algorithms have extremely slow convergence rates. To solve this problem, a number of adaptive filtering structures, based on affine subspace projections [3,4], data reusing adaptive algorithms [5,6], block adaptive filters [2] and multi rate techniques [7,8] have been proposed in the literatures. In all these algorithms, the selected fixed step-size can change the convergence and the steady-state mean square error (MSE). It is well known that the steady-state MSE decreases when the step-size decreases, while the convergence speed increases when the step-size increases. By optimally selecting the step-size during the adaptation, we can * Correspondence: [email protected] Faculty of Electrical and Computer Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran
obtain both fast convergence rates and low steady-state MSE. These selections are based on various criteria. In [9], squared instantaneous errors were used. To improve noise immunity under Gaussian noise, the squared autocorrelation of errors at adjacent times was used in [10], and in [11], the fourth order cumulant of instantaneous error was adopted. In [12], two adaptive step-size gradient adaptive filters were presented. In these algorithms, the step sizes were changed using a gradient descent algorithm designed to m
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